Spatial Econometric Analysis 1 Kuan-Pin Lin Portland State University

Introduction Spatial Data Spatial Dependence Cross Section Panel Data Spatial Heterogeneity Spatial Correlation

Spatial Dependence Least Squares Estimator

Spatial Dependence Nonparametric Treatment Robust Inference Spatial Heteroscedasticity Autocorrelation Variance-Covariance Matrix

Spatial Dependence Nonparametric Treatment SHAC Estimator Kernel Function Normalized Distance

Spatial Dependence Parametric Representation Spatial Weights Matrix Spatial Contiguity Geographical Distance First Law of Geography: Everything is related to everything else, but near things are more related than distant things. K-Nearest Neighbors

Spatial Dependence Parametric Representation Characteristics of Spatial Weights Matrix Sparseness Weights Distribution Eigenvalues Higher-Order of Spatial Weights Matrix W2, W3, … Redundandency Circularity

Spatial Weights Matrix An Example 3x3 Rook Contiguity List of 9 Observations with 1-st Order Contiguity, #NZ=24 1 2 3 4 5 6 7 8 9 1 2,4 2 1,3,5 3 2,6 4 1,5,7 5 2,4,6,8 6 3,5,9 7 4,8 8 5,7,9 9 6,8

W 1st-Order Contiguity (Symmetric) 1

W All-Order Contiguity (Symmetric) 1 2 3 4

An Example of Kernel Weights K = 1/(ii’ + W) 1/2 1/3 1/4 1/5

W1 Non-Symmetric Row-Standardized 1/2 1/3 1/4

W2 Non-Symmetric Row-Standardized 1/3 1/4

Oregon Counties

U. S. States

Spatial Lag Variables Spatial Independent Variables Spatial Dependent Variables Spatial Error Variables

Spatial Econometric Models Linear Regression Model with Spatial Variables Spatial Exogenous Model Spatial Lag Model Spatial Error Model Spatial Mixed Model

Examples Anselin (1988): Crime Equation Basic Model (Crime Rate) = a + b (Family Income) + g (Housing Value) + e Spatial Lag Model (Crime Rate) = a + b (Family Income) + g (Housing Value) + l W (Crime Rate) + e Spatial Error Model (Crime Rate) = a + b (Family Income) + g (Housing Value) + e e = r We + u Data (anselin.txt, anselin_w.txt)

Examples Ertur and Kosh (2007): International Technological Interdependence and Spatial Externalities 91 countries, growth convergence in 36 years (1960-1995) Spatial Lag Solow Growth Model ln(y(t)) - ln(y(0)) = a + b ln(y(0)) + g ln(s) + g ln(n+g+d) + l W ln(y(t)) - ln(y(0))) + e Data (data-ek.txt)

References L. Anselin, Spatial Econometrics: Methods and Models. Kluwer Academic Publishers, Boston, 1988. L. Anselin. “Spatial Econometrics,” In T.C. Mills and K. Patterson (Eds.), Palgrave Handbook of Econometrics: Volume 1, Econometric Theory. Basingstoke, Palgrave Macmillan, 2006: 901-969. L. Anselin, “Under the Hood: Issues in the Specification and Interpretation of Spatial Regression Models,” Agricultural Economics 17 (3), 2002: 247-267. T.G. Conley, “Spatial Econometrics” Entry for New Palgrave Dictionary of Economics, 2nd Edition, S Durlauf and L Blume, eds. (May 2008). C. Ertur and W. Kosh, “Growth, Technological Interdependence, Spatial Externalities: Theory and Evidence,” Journal of Econometrics, 2007. J. LeSage and R.K. Pace, Introduction to Spatial Econometrics, Chapman & Hall, CRC Press, 2009. H. Kelejian and I.R. Prucha, “HAC Estimation in a Spatial Framework,” Journal of Econometrics, 140: 131-154.